I have considered regression analysis of case-control data where a binary exposure is subject to pooling and the pooled measurement is dichotomized to indicate either that no subjects in the pool are exposed or that some are exposed, without revealing further information about the exposed subjects in the latter case. The pooling process is stratified on the disease status and possibly other variables but is otherwise assumed random. Methods are proposed for estimating parameters in a prospective regression model, and are evaluated in simulation experiments based on a real study of colorectal cancer. Numerical results show that the proposed methods perform reasonably well in realistic settings and that pooling can lead to sizable gains in cost-efficiency. Recommendations are made with regard to the proper design of pooled case-control studies.